Hi and welcome to WAB. Ellkebe
A new pond will always have algae especially if you filled it with tap water.
The bales of straw you get from the pond centre are not that big not like a bale you use for horse bedding.
I would put lots of oxygenating plants and marginals like yellow flag irises and a deep water plant like a water lilly. You need plants to take up extra nutrients from the water. I throw a bag of supermarket watercress into my pond this helps keep the weed down.
You need to starve the blanket weed..
Keep removing it as you are.
But don't worry too much as wildlife actually like the cover of it.
hope this helps..